Metamath Proof Explorer

Theorem zaddcld

Description: Closure of addition of integers. (Contributed by Mario Carneiro, 28-May-2016)

Ref Expression
Hypotheses zred.1 φ A
zaddcld.1 φ B
Assertion zaddcld φ A + B


Step Hyp Ref Expression
1 zred.1 φ A
2 zaddcld.1 φ B
3 zaddcl A B A + B
4 1 2 3 syl2anc φ A + B